EE290C – Spring 2011Lecture 5: Equalization TechniquesElad AlonDept. of EECSEE290C Lecture 5 20 2 4 6 8 10-60-50-40-30-20-100frequency [GHz]Attenuation [dB]9" FR4, via stub26" FR4,via stub26" FR49" FR4Link ChannelsEE290C Lecture 5 3• Channel is band-limited• I.e., dispersive (low pass)• Short TX pulses get spread out• Low latency• Also get reflections• Z mismatches, connectors, etc.• Longer latency0 1 2 300.20.40.60.81nspulse responseTsymbol=160psInter-Symbol InterferenceEE290C Lecture 5 4Why ISI Matters• First sample doesn’t even reach RX threshold• Suffers ISI from all previous zero bits• Middle sample hardly different from first • 0.2 trailing ISI (from previous symbol) and 0.1 leading ISI (from next symbol) 0 2 4 6 8 10 12 14 16 1800.20.40.60.81Symbol timeAmplitudeEye DiagramEE290C Lecture 5 5• Basic goal is to “flatten” channel response• I.e., in time domain, get back our nice clean pulse• For low-pass channel, equalizer boosts high frequencies+=EqualizationEE290C Lecture 5 6• Equalization been around for a very long time…• What makes electrical interfaces unique:• Performance • Power and area constraintsHistoryEE290C Lecture 5 7• More alphabet soup…• CTLE, ZFE, DFE, RX FIR, MMSE, …• Three basic distinctions:• Linear vs. Non-Linear• Continuous Time vs. Discrete Time • Minimize ISI vs. Minimize ISI + NoiseEqualizer Types EE290C Lecture 5 8Continuous Time Linear Equalizer (CTLE)EE290C Lecture 5 9CTLE Implementation, LimitationsEE290C Lecture 5 10Linear FIR EE290C Lecture 5 11Transmitter FIR ExampleTxDataCausaltapsAnticausal taps0.0 0.3 0.6 0.9 1.2-0.3-0.10.10.30.50.7UnequalizedEqualization PulseEnd of Linetime (ns)Voltage0.0 0.3 0.6 0.9 1.20.0 0.3 0.6 0.9 1.2-0.3-0.10.10.30.50.7UnequalizedEqualization PulseEnd of Linetime (ns)VoltageEE290C Lecture 5 12Setting the Coefficients• Assume channel response is known for now• See later how to estimate it• Most basic approach: zero-forcing (ZFE)Single-bit Channel ResponseEqualizedResponseEE290C Lecture 5 13ZFE Setting Formulation (Math…)EE290C Lecture 5 14“Zero-Forcing”: Desired ResponseEE290C Lecture 5 15Final Coefficients: Least SquaresEE290C Lecture 5 16Transmitter FIR RevisitedTxDataCausaltapsAnticausal taps0.0 0.3 0.6 0.9 1.2-0.3-0.10.10.30.50.7UnequalizedEqualization PulseEnd of Linetime (ns)Voltage0.0 0.3 0.6 0.9 1.20.0 0.3 0.6 0.9 1.2-0.3-0.10.10.30.50.7UnequalizedEqualization PulseEnd of Linetime (ns)Voltage• Can’t generally use ZFE result directly• TX has a peak swing constraint• At same max. swing, RX amplitude reduced• Is this a problem?EE290C Lecture 5 17The Fundamental Issue: Noise0 0.5 1 1.5 2 2.5-25-20-15-10-50frequency [GHz]Attenuation [dB]equalizedunequalized• ZFE eliminates ISI• But increases magnitude of noise relative to signal• “Noise enhancement”• Particularly bad on channels with notches• TX/RX eq. needs large atten./gain EE290C Lecture 5 18An Alternate Approach: MMSE• Don’t just cancel ISI• Find optimal balance between noise and ISI• Minimum Mean Squared Equalizer:EE290C Lecture 5 19MMSE vs. ZFE, Limitations• MMSE allows residual ISI• But amplifies noise less1 2 3 4 5 6 7 8 9 10 1100.20.40.60.81Symbol NumberNormalized AmplitideUnequalizedZFEMMSE• Unfortunately, MMSE not so straightforward to apply in links• Harder to adapt (more later)• Noise may not be knownEE290C Lecture 5 20Good News: There Is Another Way…• Once you know which bit was transmitted• You also know exactly what ISI that bit will cause• Why not directly cancel the ISI you know is coming?0 2 4 6 8 10 12 14 16 1800.20.40.60.81Symbol timeAmplitudeEE290C Lecture 5 21Decision Feedback Equalization (DFE)timePulse responseRX_inFIR Filter• Key advantage: no noise enhancement• Feedback signal based on “perfect” digital bits• ISI subtracted based on those bitsEE290C Lecture 5 22DFE IssuesRX_in• Only handles post-cursors• May still need linear (feedforward) filter for pre-cursors• What happens when RX makes a mistake?EE290C Lecture 5 23DFE Issues: TimingRX_in• Need to do all of the following in at most 1UI:• Resolve the (small) bit• Scale the bit by the coefficient• Sum the new analog valueEE290C Lecture 5 24Pulse Shape InteractionRX_in• Ideal DFE would actually settle within 0.5UI• Otherwise affects edge position• FIR filter can have same issue• Fixing it requires an over-sampled (fractional) equalizerEE290C Lecture 5 25Fractional Equalization1 2 3 4 5 6 7 8 9 1000.20.40.60.81Symbol NumberNormalized AmplitudeSymbol-spaced2x